Solution:

The young lady was presented with a bill which belonged to the elderly woman. She had asked the waiter to collect the bill from her daughter.

Solution:

41312432

Solution:

She is near the trunk of the tree as shown below.

Solution:

This can be done if you draw a five pointed star and place the balls on the corners and intersection points. See the figure to understand better.

Solution:

Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.

So either A or B will speak up first depending on the situation.

Solution:

See the colored sticks in the picture. We have moved those sticks in the position given in the second image corresponding with the color.

Solution:

Let us denote the number of boys as 'p' and the number of girls as 'q'.

The first statement says that each boy has equal numbers of brothers and sisters
(p - 1) = q
=> p - q = 1 ------- (a)

The second statement says that every girl has twice as many brothers as that of sisters
2 (q - 1) = p
=> 2q - p = 2 ------- (b)

By solving (a) and (b)
We get q as 3 and p as 4.

Therefore, there are 4 boys and 3 girls in the family.

Solution:

It can be solved as below.

Solution:

One of the cop will move clockwise while the other will move anti-clockwise every day. In such a manner, they will catch the thief in minimum seven days.

Solution:

28 =>1+2+4+7+14

cannot be 1 (as number cannot be included)

Solution:

Put one red marble in one box and all other marbles in the 2nd box.

Probability :
50 + 24/49